From: Allin Cottrell (cottrell@wfu.edu)
Date: Mon Nov 22 2004 - 23:56:16 EST
On Sun, 21 Nov 2004, Rakesh Bhandari wrote:
> [W]hat determines the money put in circulation by the Fed or on
> what basis does the Fed attempt to regulate the money in
> circulation?
My take on the matter, as I have said, is that the Greenspan Fed is
primarily concerned to stablize CPI inflation around a small
positive rate, and to the extent they follow the prices of narrower
baskets of commodities they are for the most part using these as
putative advance indicators of general inflation/deflation.
You, on the other hand, claim that the Fed is trying to stabilize
the price of a small basket of commodities in which gold features
prominently.
Let's look at the data. We can define a "control error", et, equal
to the gap, each period, between the price of a chosen commodity
basket and the target price, which could either be a constant or a
smooth trend. If there were just one commodity at issue the gap
would be
et = a0 + a1 * t - Pt
where Pt is the price of the given commodity in period t. If the
price were controlled perfectly, et would = 0 in all periods.
If there are three commodities -- you mentioned gold, oil and wheat
-- the counterpart equation is
et = a0 + a1 * t - (b1 * Pgt + b2 * Pot + b3 * Pwt)
where Pgt is the price of gold in period t, Pot is the oil price and
Pwt is the wheat price. The b's are the weights on these
commodities in the basket.
We can obtain estimates of the variance of the control error, on the
assumption that the average error is 0, by inverting these equations
and applying least squares. That is, one estimates
1 = -(a1/a0) * t + (b1/a0) * Pgt + (b2/a0) * Pot
+ (b3/a0) * Pwt + et/a0
The dependent variable is just a constant. We can't get estimates
of all the parameters, but we can find their relative magnitudes and
can compare the relative variance of the control error across
baskets. (Just to explore the math, note that if there were a
linear combination of Pg, Po and Pw that was actually constant over
time, or followed an exact trend, the above regression would produce
a perfect fit; and in general it will "choose" basket weights so as
to minimize the sum of squared control errors.)
I did the econometrics using the price of gold on the London market,
the price of Saudi light crude, and the price of hard red winter
wheat, annual average data for the years 1988 (when Greenspan became
Fed Chairman) to 2003. I converted all variables to indices with a
base of 100 in 1988, and made the dependent variable equal 100.
(Besides the linear trend I included the square of time for good
measure.)
The estimated variance of the control error for this 3-commodity
basket was 91.23 (that is, this was the residual variance from the
regression indicated above). I then repeated the exercise using the
CPI-U as the basket (again, scaled to a base of 100 in 1988 and
using 100 as the dependent variable). The control error variance
was 1.06, smaller by a factor of 86 or so. If you prefer to look at
the sum of squared errors, the respective figures were 1003.5
(3-commodity basket) and 13.8 (CPI).
My conclusion is that there is no linear combination of the prices
of gold, oil and wheat that has been *anything like* as stable
around a trend as the CPI, over the last 16 years. If it is the
price of such a basket that Greenspan has been trying to stabilize,
then he has failed abjectly. On the other hand, if he has been
trying to stabilize CPI inflation then he has done a pretty good
job.
Allin
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